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2 Answers
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I imagine individual differences in enjoyment derived from horror films would be multifaceted as with most preferences regarding consumption of different media. Some of the research mentions how males, teenagers/young adults, sensation seekers, and those who have a history of exposure to horror films (although this may be both cause and effect) tend to like horror films more.

Sensation seeking is a personality trait defined by the search for
experiences and feelings, that are "varied, novel, complex and
intense", and by the readiness to "take physical, social, legal, and
financial risks for the sake of such experiences." (Zuckerman, 2009). Risk is not an
essential part of the trait, as many activities associated with it are
not risky.

Zuckerman discusses the psychology of horror films in this video (see transcript here). He frames sensation seeking in terms of habituation. Thus, the more horror films that a person has seen, the more intense the horror would need to be in order to induce the same rewarding level of arousal.

Exploring the concept of sensation seeking may also move you more towards a more primary concept of why people seek such arousal inducing experiences. You could for instance read Roberti's (2004) literature review of the biological and behavioural correlates of sensation seeking. In particular, see section 4 on biological characteristics related to sensation seeking:

A survey was conducted to determine the antecedents of the exposure to
and appeal of horror films. Audience members leaving the theater after
viewing Halloween II were interviewed using a questionnaire that
contained measures of specific reasons for liking horror films as well
as measures of several individual-difference variables. A model
emerged from structural equation analysis indicating that three
important factors in the appeal of horror films are (a) the audience's
desire to experience the satisfying resolutions usually provided in
these films, (b) the audience's desire to see the destruction often
found in these films, and (c) the sensation-seeking personality traits
of audience members for these films. In addition, age and gender were
important predictors. Horror films were enjoyed more by males and by
younger viewers.

Several studies have attempted to investigate the relationship
between the attraction to horror films and sensation seeking. The
first attempt to look at this issue was reported by Sparks
(1984), who correlated his own 20-item scale measuring Enjoyment of
Frightening Films (EFF) with the Sensation-Seeking Scale, and found
an overall positive correlation between the two for both males (r=
.22,p= .01) and females (r = .28, p = .01). A second study (Tamborini
& Stiff, 1984) also found an association between the liking of horror
films and a measure of sensation seeking computed from the
combination of disinhibition, experience seeking, and thrill and
adventure seeking scores (r= .14,p= .05). Finally, Edwards (1984)
found a strong correlation between the entire Sensation-Seeking Scale
and interest in horror movies (r = 51, p < .001). Unfortunately, the
articles by Sparks (1984) and Tamborini and Stiff (1984) do not
report the correlations between the individual subdimensions of
the Sensation-Seeking Scale and their measures of attraction to
horror films. This information is of particular interest to us if we
want to understand the appeal found in horror since these
subdimensions are thought to be unique. The study by Edwards (1984)
does provide information in this regard, however. According to
Edwards, each of the subdimensions is correlated to interest in
horror films with disinhibition having the strongest relationship (r
= .54, p < .001), followed by boredom susceptibility (r = .41,p < .001), experience seeking (r= .39,p < .001), and thrill and adventure
seeking (r= .24, P < .01).

I would speculate that the answer lies within mirror neurons. By watching the film, our mirror neurons are firing, so we have that empathatic connection to the film.

When you see a person throwing darts, at the same time, your mirror neurons are firing, and the part of your brain that would control your hand movements (ie, thorwing a dart) are activated, although the signal doesn't actually go to the muscles in your hands to start moving....

When we watch a horror film, and we see a person in the movie feeling tremendous fear, our mirror neurons fire up, and we feel that same emotion, to an extent.

Not to mention that often times, when watching a movie, we enter a hypnotic state, which in of itself is a "flight" mechanism.

So, when we watch the horror films, we are subconsciously experiencing the emotions portrayed, and depending on how deeply engrossed we are in the movie (you can read that as "depeding on how deeply hypnotized we are while watching the movie") it can trigger a fight/flight response.

The second part of your question, why can one person enjoy this and another person does not... That is a more complex question, as there are too many variables. What, specifically, do they like?

For example, let's take coconuts. Some people love coconuts. Why do they love coconuts, but others cannot stand them? What memories are triggered by the scent, taste, feel of the coconut? For me, I cannot stand the texture, and the taste is not exciting, so in general I do not like coconuts, and I avoid food that has coconut. But my friend absolutely LOVES coconuts. Why does he like coconuts?